How to extend scalars of a MeatAxe $kG$-module $M$ given in GAP?

Question

Let $G$ be a finite group. Suppose $k:=\mathbb{F}_5$, let char$(k)\mid |G|$, and let $M$ be a $kG$-module given in GAP, as in the following example:

G:=Group((1,2),(1,2,3,4,5));
M:=RegularModule(G,GF(5))[2];

Question:

How can one define a new module $N$ in the MeatAxe of GAP such that $N=\mathbb{F}_{625}\otimes_{k} M$ ?

The module above is only an example. I would be interested in doing this with any finite-dimensional $kG$-module in GAP.

Is this already implemented somewhere (via Conway-polynomials) ?

I am using GAP 4.11.0 and have also installed the Shared C MeatAxe (see https://users.fmi.uni-jena.de/~king/SharedMeatAxe/).

Thank you very much for the help.

Answer 1

A MeatAxe module in GAP is defined by the matrices describing an algebra action (the component .generators) and the field. You can simply take the existing matrices of a module and define a new module over a larger field:

gap> N:=GModuleByMats(M.generators, GF(625));;

(In your example all irreducible modules are absolutely irreducible, so you will not see much difference of results.)